This invention relates to interferometers, e.g., linear and angular displacement measuring, that measure linear and angular displacements of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system.
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from a reference object.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams.
A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/λ, where v is the relative speed of the measurement and reference objects, λ is usually the wavelength of the measurement beam, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the phase of the measured interference signal correspond to changes in the relative position of the measurement object, e.g., a change in phase of 2π corresponds substantially to a distance change L of λ/(2np). Distance 2L is a round-trip distance change or the change in distance to and from a stage that includes the measurement object. In other words, the phase Φ, ideally, is directly proportional to L, and can be expressed asΦ=2pkL cos2 θ  (1)for a plane mirror interferometer, e.g., a high stability plane mirror interferometer, where
  k  =            2      ⁢      π      ⁢                          ⁢      n        λ  and θ is the orientation of the measurement object with respect to a nominal axis of the interferometer. This axis can be determined from the orientation of the measurement object where Φ is maximized. Where θ is small, Equation (1) can be approximated byΦ=2pkL(1−θ2)  (2)
Unfortunately, the observable interference phase, {tilde over (Φ)}, is not always identically equal to phase Φ. Many interferometers include, for example, non-linearities such as those known as “cyclic errors.” The cyclic errors can be expressed as contributions to the observable phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in for example optical path length 2pnL. A first order cyclic error in phase has, for example, a sinusoidal dependence on (4πpnL)/λ and a second order cyclic error in phase has, for example, a sinusoidal dependence on 2(4πpnL)/λ. Higher order cyclic errors can also be present as well as sub-harmonic cyclic errors and cyclic errors that have a sinusoidal dependence of other phase parameters of an interferometer system comprising detectors and signal processing electronics.
There are in addition to the cyclic errors, non-cyclic errors. Non-cyclic errors include both non-linear non-cyclic errors and geometric non-cycle errors.
An example of a source of a non-linear non-cyclic error is the diffraction of optical beams in the measurement paths of an interferometer. Non-cyclic error due to diffraction has been determined for example by analysis of the behavior of a system such as found in the work of J.-P. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szöke, F. Zernike, P. H. Lee, and A. Javan, “Accurate Laser Wavelength Measurement With A Precision Two-Beam Scanning Michelson Interferometer,” Applied Optics, 20(5), 736-757, 1981.
A second source of non-cyclic error is the effect of “beam shearing” of optical beams across interferometer elements and the lateral shearing of reference and measurement beams one with respect to the other. Beam shearing can be caused, for example, by a change in direction of propagation of the input beam to an interferometer or a change in orientation of the object mirror in a double pass plane mirror interferometer such as a differential plane mirror interferometer (DPMI) or a high stability plane mirror interferometer (HSPMI).
Geometric non-cyclic errors (or simply “geometric errors”) refers to errors in interferometry measurements that arise from a deviation of one or more beams from a nominal beam path and cause an optical path deviation from the assumed optical path. Conventionally, the position of a measurement object in a reference frame is calculated assuming that the beams propagate along nominal paths in the reference frame. Thus, while a measured interference phase is proportional to the optical path difference between the measurement and reference beams, a geometric error causes a deviation in the determined position of the measurement object in the reference frame from its actual position.
Geometric errors are caused by imperfections in the interferometer optics, the measurement object, or the source. For example, surface or bulk imperfections in one or more optics in the interferometer or the measurement object can cause geometric errors. Surface or bulk imperfections can be caused by, e.g., bulk inhomogeneities or errors in a surface figure. Furthermore, misalignment of one or more optical components in the interferometer or of the interferometer light source can cause geometric errors.
The effect of contributions to the observable phase due to cyclic and non-cyclic errors can be reduced by quantifying these errors and correcting subsequent measurements with this data. Different techniques for quantifying cyclic errors are described in commonly owned U.S. Pat. Nos. 6,252,668, 6,246,481, 6,137,574, and U.S. patent application Ser. No. 10/287,898 entitled “INTERFEROMETRIC CYCLIC ERROR COMPENSATION” filed Nov. 5, 2002 by Henry A. Hill, the entire contents each of which are incorporated herein by reference. In order to compensate for these contributions, cyclic error compensating systems and methods can be used to determine a cyclic error function characterizing the cyclic error contribution to the observed phase. Examples of apparatus and details of methods that can be used to characterize non-cyclic errors in interferometers and interferometer components are described in U.S. patent application Ser. No. 10/366,587 entitled “CHARACTERIZATION AND COMPENSATION OF NON-CYCLIC ERRORS IN INTERFEROMETRY SYSTEMS,” to Henry A. Hill, filed on Feb. 12, 2003, the entire contents of which are incorporated herein by reference.